Electric wave filter



Patented May 15, 1934 ELECTRIC WAVE FILTER Andreas Jaumann, Berlin-Charlottenburg, Germany, assignor to Siemens & Halske, Aktiengesellschaft, Siemensstadt, near Berlin, Germany, a corporation of Germany Application October 3, 1931, Serial No. 566,750 In Germany October 4, 1930 6 Claims.

My present invention relates to improvements in electric Wave filters of the type disclosed in Letters Patent of the United States No. 1,882,631, dated October 11, 1932. Said patent relates to wave filters distinguished by a considerable steepness of the attenuation curve at the boundaries of the pass-bands. The wave filters of said patent are built up of individual partial filters or component filters with a resonance curve having a :lo plurality of waves and approximately equal passalternately of opposite polarity. My present invention has for its purpose to improve wave filters of the above indicated type, as regards the character of their attenuation curves and also with respect to the course of their characteristic impedance. One object of these improvements is to provide means whereby in filters of the said type, in the case of relatively wide pass-bands, the steepness of the attenuation curve at the boundaries of the pass-band and the symmetry degree of said curve may be predetermined as desired, by a proper dimensioning and connection of the individual filters or component filters which compose a wave filter of the type set forth in the aforesaid Letters Patent. Another feature of the present invention has for its object to smooth the characteristic wave impedance of the wave filter, within the pass-band, by a particular dimensioning and connection of said component filters.

The invention will now be described in detail with reference to the accompanying drawing, and the novelty will then be pointed out in the appended claims.

In the said drawing, Fig. 1 is a diagram showing how, by variously dimensioning the filter elements I am able to predetermine as desired, not only the steepness of the attenuation curve at the boundaries of the pass-band, but also the symmetry degree of such curve within the cutoff range; Figs. 2 and 2d are diagrammatic views of two typical forms of wave filters in which my invention may be embodied; and Fig. 3 is a diagram illustrating the determination of the Wave impedance in filters constructed according to my invention.

The constituent elements of wave filters of the type shown in Letters Patent 1,882,631 and to which my present invention may be applied, are indicated in the two examples illustrated by Figs. 2 and 2a, of which Fig. 2 is a reproduction of Fig. 24 of said patent, with the addition of certain reference characters.

In each of these two figures, I and II designate the input terminals, and I, II the output terminals. In Fig. 2, the Wave filter consists of two component filters each having two branches with a condenser and acoil connected in series in each branch. One of these component filters consists of the branch containing the condenser C1 and the coil L1 and of the branch containing the condenser C4 and the coil L4. The other component filter consists of the branch containing the condenser C3 and the coil L3, and of the branch containing the condenser C2 and the coil L2. The output terminal I is connected with all the condensers, on the side opposite to the respective coils, the other ends of these coils being connected with each other as indicated, a coil T which forms part of this connection being located between the branches containing the coils L3 and L4 respectively. The midpoint of this coil T is connected with the output terminal II, while the ends of the coil T receive impulses through the input terminals I and II respectively. 0

The wave filter illustrated by Fig. 2a differs from the one shown in Fig. 2 by having three component filters instead of two, and by having the input terminals I and II connected with the primary T of a transformer the secondary coil T of which is connected with the output terminal II and with the coils L0 L1 L2 L3 L4 L5 of the component filter branches in the same manner as in Fig. 2. The first component filter of Fig. 2a comprises the branch containing the condenser C0 and the coil Lo, and the branch containing the condenser C5 and the coil L5; the second component filter comprises the two branches containing the condensers and coils designated by reference characters C and L bearing the indices 1 and 4 respectively; and the third component filter comprises the two branches containing the condensers and coils designated by reference characters C and L bearing the indices 2 and 3 respectively.

' It will be noted that both in Fig. 2 and in Fig. 2a, the terminal of one branch of each component filter is on one side of the coil'I, and the corresponding terminal of the other branch on the opposite side thereof, so that at any particular instant, those terminals of each pair of branches belonging to the same component filter which are on one side (the lower side, on which the coil T is located) will be of opposite polarity. In these two embodiments, furthermore, the two branches of the same component filter are connected in parallel, and each branch contains two, impedance elements (C, L) connected in series; the resistances of these two impedance elements have reciprocal values, and in their simplest form may consist of coils and condensers. The several component filters are designed to have practically the same pass-band centers, and different resonance curves.

There are two features the consideration of which is of particular importance in my invention. The attenuation characteristic may be improved by modifying the steepness of the attenuation curve, without altering its symmetry; such a symmetrical attenuation curve is indicated by the dotted lines 1, 1 in Fig. 1. In the case of narrow pass-bands, a modification of the steepness of the attenuation curve is frequently sufficient to secure attenuation characteristics meeting practical requirements. In some cases, however, and particularly when the width of the passband is comparatively large, it has been found that in order to obtain the best results, it is not sufficient to simply modify the steepness of the attenuation curve, and in such cases I employ, in conjunction with the feature just explained, a second feature which consists in giving the attenuation curve an unsymmetrical shape relatively to the center of'the pass-band. Attenuation curves embodying both of these features are shown in Fig. l at 2, 2 and 3, 3. In this way a higher attenuation can be obtained at one of the limits of'the transmission range of the wave filter than at the other limit, and this result is particularly desirable in the case of a comparatively great width of the pass-band.

The improved results of my present invention are obtained by employing a compound filter of the type referred to above and so designing the parts thereof as to secure not only the desired steepness of the attenuation curve, but the desired difference (asymmetry) of the two branches of the said curve relatively to the center of the pass-band. For this purpose, proper values, determined as will be set forth hereinafter, are given to the various elements of the filter, the polarities of the elements being as explained above. When, as in the examples illustrated by Figs. 2 and 211, each branch of a component filter contains a coil and a condenser whose resistances have reciprocal values, the resonance frequencies of the several branches will be given values in accorda ce with a definite law which may be expressed graphically as a function or curve of an arithmetical distribution with uniform rise and curvature, i. e. a function which may be represented by a convergent series beginning with the terms a+b, 30+. if the band width is chosen as the origin of the coordinate system. In this case, the steepness of the attenuation curve is determined by a number of parameters one less than the number of component filters, that is to say, if there are m component filters, there m-1 parameters R1, 762 icm 1 governing the steepness of the attenuation curve. The degree of symmetry or rather asymmetry of said curve is determined essentially by a parameter k. I have explained below how these parameters 10 and A are calculated.

According to another feature of my invention, the characteristic impedance of the filter is smoothed out by using a component filter having the same band-width as that one of the other component filters which has the greatest band width, but giving the first of these two component filters of like band-width, a different characteristic impedance curve and on one side a polarity different from that of the second component filter.

An arithmetic distribution of the resonance frequencies of the component filter branches implies equal intervals between the two resonance frequencies of the same component filter and the center of the pass-band. Such a distribution is obtained readily when the pass-band is comparatively narrow. However, in the case of relatively wide pass-bands, it is necessary to select definite resonance frequencies, in order to facilitate computing the values to be given to the elements of the component filters, according to the desired attenuation curve. The selection of the resonance frequencies may be effected according to any distribution law which, in the limit case of narrow band-widths will yield resonance frequencies merging into one another and into an arithmetical distribution, as referred to above. In this case, the several component filters may be given approximately equal pass-band centers even when the relative band-width is comparatively large.

Various distribution laws will meet the general conditions just set forth. As particular instances I will mention the following:

(1) The geometrical distribution of the resonance frequencies according to the function or equation where w is the variable resonance frequency of th branches of the component filters, E2 the mean frequency of the pass-band of the entire filter, e the well-known base of the natural logarithms (c=:2.'71828l828.- and as a value determined from the above equation as equal to log. nat. (ii-10g. hat. 9.

(2) The arithmetical distribution of the squares of the resonance frequencies according to the function or equation (3) The arithmetical distribution of the reciprocal squares of the resonance frequencies ac cording to the function or equation With any one of these distribution laws, it is possible to determine arbitrary values for the degree of symmetry (or asymmetry) of the attenuation curves, such values being expressed in terms of a: as an independent variable, with the aid of a parameter x to be explained below, and also for the steepness of the attenuation curve, with the aid of the parameters I01, 702 km-i (m being the number of component filters) likewise explained below. In the case of i=1, the attenuation curve is symmetrical; for any other value of A, the attenuation curve is asymmetrical. The parameter A controls the electrical dimensioning of the coils L and condensers C, while the parameters 70 control the special distribution of the resonance frequencies within the limits of .the distribution law chosen in each particular case.

I will now set forth in detail two examples of calculations for determining the elements of filters such as shown in Figs. 2 and 2a respectively.

Example A Employing a filter which consists of two component filters as in Fig. 2 and using the distribution law given above under 1), w=Qe designating by b the relative band width, and giving as successively the values b kb (where is is betWeen'O and 1) we have the following values (in the order of their magnitudes) for the resonance frequencies on ma m3 m4 of the four branches which contain the condensers C and coils L designated by the respective indices:

from which we derive The absolute band Width of the filter is given by (1 cosh B the difference (wk-ml and is equal to the absolute band width of the component filter whose branches have the resonance frequencies m1 and 04 respectively. The other component filter, whose branches have the resonance frequencies as and ms respectively for approximately the same pass-band center, has a relative band width differing by the factor is from the relative band width of the first-mentioned component filter. By choosing the resonance frequencies in accordance with the rule given above, the points of infinity are shifted so as to obtain variations in the steepness of the attenuation curve. As stated hereinbefore, the parameter k governs the steepness of the said curve. If the symmetry of this curve is also to be varied, I employ the additional parameter where L1 C1 and L4 C4 are the values of the inductances and of the capacities of the component (the value 1 :1 being at the center of the pass band). The ordinates in Fig. 1 represent values of the factor [3, expressed in nepers (attenuation units). If we choose the value A:1, the resulting attenuation curve will have two branches symmetrical to the ordinate at the point whose abscissa is the zero of the a: scale (or the 1 of the 1 scale). If simultaneously with A=1, we choose lc=.5, the attenuation curve will have the shape indicated at 1. If It is increased to .56, the attenuation curve will become steeper at the bandpass limits, as indicated by the curve 2 in Fig. 1, the two branches of this curve being symmetrical, since we still choose A=1. If however the value of A differs from 1, the attenuation curve will no longer be symmetrical. For instance, with 70:.56 (same value as for curve 2) and A=1.034, the attenuation curve will assume the shape shown at 3 in Fig. 1. It will be seen that this curve indicates an attenuation of 3.3 nepers outside the pass-band, on the lower side thereof, and more than 6 nepers in the upper portion of the frequency range. The band-width of the filter itself is not altered by varying the values of k and A. I have found that particularly advantageous forms of the attenuation curves are obtained by selecting A between the approximate limits of .9 and 1.1, and lo between the limits of .5 and .6.

The attenuation curves would be calculated with the aid of the equation sinh (x+lta) sinh (x-a) sinh (xka) sinh (x-I- a) sinh (x-l-ka) sinh (xa))\ sinh (x-ka) sinh (x-l-a) where a is the relative band Width of the entire filter.

sinh x (2) sinh a where Z0 is the characteristic impedance at the center of the pass-band (point 0 of the a: scale and 1 of the 1; scale). Since the course of the characteristic impedance is not altered by varying is and A, plotting of the attenuation curves will sufiice to furnish a criterion as to: what values L of k and A will be best suited for practical purposes. I y

In a concrete case, there would be given the resonance frequency values 021 and 604 indicating the limits or boundaries of the pass-band, and the value Z0 of the characteristic impedance at the center of the pass-band. The relation of this value Z0 tothe mean characteristic impedance Z (which in the adjustment must be equal to the terminal resistances, for instance those .of the line connected with the filter) is expressed by the equation in view of the approximately elliptical shape of the characteristic impedance curve within the limits of the pass-band.

Having plotted a number of attenuation curves according to Equation (1), so as to obtain a clear idea of the effect of different factors It and A, a

suitable selection will be made for the values of 7c and A, preferably within the limits mentioned above (70 from .5 to .6 and A from .9 to 1.1) Having thus chosen constant values for the parameters 7c and A, we calculate the mean frequency of the pass-band as the relative pass-band width as b= 2a=1og. nat p and the other two individual resonance frequencies as From the above we also derive the auxiliary magnitudes or factors sinh (1 k)a sinh a sinh (1 k)a With the aid of the above the values of the insinh (1 +k)a sinh a sinh Zka and the steepness factor substituting this in Equation (1), we obtain ductances L and of the capacities c or the four branches of the two component filters are determined as Employing a wave filter which consists of three component filters as in Fig. 2a, I will consider the case where it is desired to smooth out the characteristic impedance in the pass-band, bee sides obtaining a steeper rise of the attenuation curve. In such a case two of the component filters (those with the filter elements C5 L5 Co Lo and C4 L4 C1 L1 respectively) have equal bandwidth and are analogous in design and therefore proportional to each other withrespect to their characteristic impedance curves, such bandwidth being preferably in accordance with the largest band-width of the whole of the component filters. The two component filters of equal bandwidth are connected in parallel as shown, with alternately opposed polarity of the terminal pairs on one side of the component filters (the lower side in Fig. 2a).

As in the case of Fig. 2, we shall assume that we are using the distribution law given above under (1), w oe In this case there will apply Equations (3) and (4) which are analogous to Equations (1) and (2) respectively, but in Equations (3) and (4) a distinction is made between the pass-band width 2a of an individual component filter (having the maximum pass-band width) and the pass-band width 2A of the entire filter combination.

The first of the component filters may be considered as having the resonance frequencies mo and m5, and the second component filter as having the resonance frequencies w], and 01-1. In other words, the resonance frequencies are designated by reference characters having the same indices as the corresponding condensers C and coils L in Fig. 2a.

In addition to these two parameters A and k, with the aid of which I can calculate and plot attenuation curves of the same general character as in Fig. 1, I introduce a third parameter, n, Which determines or controls the degree of smoothnessof the characteristic impedance curve in-the pass-band. This parameter is defined by s the equation sinh a I sinh a By introducing this parameter n into Equation (4) relating to the characteristic impedance, said Equation (4) will be brought into the form sinh A (6) 31m sinh A sinh (x-i-ka) sinh (xA)-l)\ sinh (x-ka) sinh (x-l-A) rived from the electric quantities of two com? ponent filters,

as .5, the points A and B being at .25 from the zero of the at scale. Between the ordinates drawn through the points A and B, the characteristic impedance is real, outside that range it is imaginary. The several curves indicate the changes in characteristic impedance obtained by giving the parameter n different values so that n will be 0, .2, .4, .6, .8 and 1 respectively. By a properchoice of this parameter, the characteristic impedance curve may be smoothed within the pass-band, that is to say, such curve may be flattened between the two ordinates drawn through A and B, so that such flattened portion will be approximately horizontal. The diagram shows clearly that satisfactory results in this The individual resonance frequencies of the sev- From these we would calculate the four auxiliary respect will be obtained with values of n ranging about from .5 to .7. In certain cases, it may be desirable to choose n =.8, in order that the fiattening of the curve may extend to a greater width, although the approach to the horizontal will not be so close in this case, as will be evident from the diagram. The portions of the characteristic impedance curve which lie outside the pass-band show that the characteristic impedance has two zero points. These correspond to infinity points of the net-loss curve. In the case of a parallel connection of several such Wave-filters having different pass-bands, these infinity points must be taken into account, since they must not fall within the pass-band of an adjacent wave-filter.

As to A and lo, I have found that very satisfactory results are obtained with A ranging about from .9 to 1.1 and k ranging about from .5 to .6.

In a concrete case, there would be given the limit frequencies w: and on of the pass-band, the value Z0 of the approximately constant characteristic impedance; then suitable values would be chosen for the parameters k, A, and n, for instance so that the steepness factor k would lie between .5 and .6, the symmetry factor A between .9 and 1.1, and the smoothness factor 12 between .5 and .6.

From these there would be calculated the passfrom the equations sinh oz sinh a and k=k g eral branch circuits of the component filters would be Finally, from the above the several self-inductances and capacities would be figured as:

Various modifications may be made without departing from the nature of my invention as defined in the appended claims.

I claim:

1. An electric wave filter consisting of a pluthe same pass-band centers and multiresonant resonance curves, the input terminals of said filters being connected with each other, and their output terminals being likewise connected with each other, the terminal pairs on one side of the component filters being of alternately opposed polarity, and the elements of such filters having electrical dimensions such as to give the component filters inductance and capacity values which will give the attenuation curve an unsymmetrical shape exteriorly of the pass-band.

2. An electric wave filter consisting of a plurality of component filters which have practically the same pass-band centers and multiresonant resonance curves, the input terminals of said filters being connected with each other, and their output terminals being likewise connected with each other, the terminal pairs on one side of the component filters being of alternately opposed polarity, one of said component filters having a polarity and electrical connections and dimensions such as to give the characteristic impedance curve of the wave-filter a smoothed or fiattened formation within the pass-band.

3. An electric wave filter consisting-of a plurality of component filters which have practically thesame pass-band centers and multiresonant resonance curves, the input terminals of said filters being connected with each other, and their output terminals being likewise connected with each other, the terminal pairs on one side of the component filters being of alternately opposed. polarity, and the elements of such filters having electrical dimensions such as to give the component filters inductance and capacity values which will give the attenuation curve a steep formation at the limits of the pass-band and an unsymmetrical shape exteriorly of the pass-band, one of said component filters having a polarity and electrical dimensions such as to give the characteristic impedance curve of the wave-filter a smoothed or flattened formation within the pass band.

4. An electric wave filter consisting of a plurality of component filters which have practically the same pass-band centers and different resonance curves, the input terminals of said filters being connected with each other, and their output terminals being likewise connected with each other, the terminal pairs on one side of the component filters being of alternately opposed polarity, each of said component filters being composed of impedance branches connected with each other at one end, a coil connected to the other ends of said' branches, a terminal connected with the first-mentioned ends of said branches, another terminal connected with the midpoint of said coil, each of said branches containing a condenser and a coil in series connection, the resonance frequencies of the several branches conforming to a formation law represented by a function with uniform rise and curvature and depicting an arithmetic distribution, said formation law yielding a parameter determining the degree of symmetry of the attenuation curve relatively to the passband, and also yielding, as controlling the steepness of said attenuation curve, a number of other parameters which is one less than the number of component filters composing said wave-filter.

5. An electric wave filter consisting of a plurality of component filters which have practically the same pass-band centers and multiresonant resonance curves, the input terminals of said filters being connected with each other, and their output terminals being likewise connected with each other, the terminal pairs on one side of the component filters being of alternately opposed polarity, one of said component filters having the same transmission band as that one of the other component filters which has the widest transmission band, said twocomponent filters of like transmission band having different characteristic impedance curves and being connected to each other with opposite polarity.

6. An electric wave filter consisting of a plurality of component filters which have practically the same pass-band centers and different resonance curves, the input terminals of said filters being connected with each other, and their output terminals being likewise connected with each other, the terminal pairs on one side of the component filters being of alternately opposed polarity, one of said component filters having the same transmission band as that one of the other component filters which has the Widest transmission band, said two component filters of like transmission band having different characteristic impedance curves, each of said component filters being composed of impedance branches connected with each other at one end, a coil connected to the other ends of said branches, a terminal connected with the first-mentioned ends of said branches, another terminal connected with the midpoint of said coil, each of said branches con taining a condenser and a coil in series connection, the resonance frequencies of the several branches conforming to a formation law represented by a function with uniform rise and curvature and depicting an arithmetic distribution, said formation law yielding a parameter determining the degree of symmetry of the attenuation curve relatively to the pass-band, and also yielding, as controlling the steepness of said attenuation curve, a number of other parameters which is one less than the number of component filters composing said wave-filter, and an additional parameter which controls the degree of smoothness of the characteristic impedance curve.

ANDREAS JAUMANN. 

